The Laestadian Lutheran Church (LLC), the American branch of the Laestadians, defines sin by quoting Ro. 14:23 saying sin is "whatsoever is not of faith". One reason they think it's sinful is that there's a whole lot on TV and in popular music that meets that criterion. And since it is part of their mission to promote "Christian values and ethics", seeing any show or movie rated higher than G would pretty much make them hypocrites (some make exceptions for documentaries). It's not the act of watching or listening or the TV or iPod that is sinful, it's the content of what is being seen or heard.
Those who have left the Laestadian church state that there are no rules prohibiting these acts but that they are severely frowned upon. That alone can be enough to deter someone living in such a tightly knit community from going against their group's norms. See these heartfelt testimonies here, and here, and especially here.
The last link is actually a book that is free to read online. If you want an in-depth perspective from someone who knows, it's a great resource. Essentially, it is an apologetic by the author (Edwin Suominen) documenting why he left. It is as objective as an ex-insider can possibly make it. In Section 4.6, he lists and explains what might motivate these two, and a whole host of other, sins. Those motivations include: authoritarianism; Christian asceticism; societal differentiation; keeping people within the fold; selective adherence to biblical edicts; and maintaining ample material for the forgiveness of sins to work with.